Chemistry for Today: General, Organic, and Biochemistry
Chemistry for Today: General, Organic, and Biochemistry
9th Edition
ISBN: 9781305960060
Author: Spencer L. Seager, Michael R. Slabaugh, Maren S. Hansen
Publisher: Cengage Learning
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Chapter 1, Problem 1.76E
Interpretation Introduction

(a)

Interpretation:

The area and perimeter for each rectangle is to be calculated and the results are to be expressed in square centimeters and centimeters respectively. The correct number of significant figures is to be stated.

Concept introduction:

In a number, the digits which express the accurate measurement of the number are known as significant figures. It is counted starting from the first non-zero digit in the given number. Zeroes that lie between two non-zero digits are considered significant. Zeroes at the end of a number are considered non significant in the absence of a decimal point, whereas they are considered significant if there is a decimal point after it. Zeroes after a decimal point are considered significant.

Expert Solution
Check Mark

Answer to Problem 1.76E

The areas of black, red, green and orange rectangles are 124.8cm2, 48.884cm2, 8.109cm2 and 8.9896cm2 respectively. The number of significant digits in the results is 4, 5, 4 and 5 respectively. The perimeters of black, red, green and orange rectangles are 44.8cm, 45.24cm, 11.46cm and 27.8cm respectively. The number of significant digits in the results is 3, 4, 4 and 3 respectively.

Explanation of Solution

Given

The length and width of the black rectangle are l=12.00cm and w=10.40cm respectively.

The length and width of the red rectangle are l=20.20cm and w=2.42cm respectively.

The length and width of the green rectangle are l=3.18cm and w=2.55cm respectively.

The length and width of the orange rectangle are l=13.22cm and w=0.68cm respectively.

The formula to calculate the area of a rectangle is given below.

Area=l×w …(1)

Where,

l is the length

w is the width

The area of black rectangle is calculated as shown below.

Area=l×w=12.00×10.40=124.8cm2

The number of significant digits in the result is 4.

The area of red rectangle is calculated as shown below.

Area=l×w=20.20×2.42=48.884cm2

The number of significant digits in the result is 5.

The area of green rectangle is calculated as shown below.

Area=l×w=3.18×2.55=8.109cm2

The number of significant digits in the result is 4.

The area of orange rectangle is calculated as shown below.

Area=l×w=13.22×0.68=8.9896cm2

The number of significant digits in the result is 5.

The formula to calculate the perimeter of a rectangle is given below.

Perimeter=Sumofallfoursides=2(l+w) …(2)

Where,

l is the length

w is the width

The perimeter of black rectangle is calculated as shown below.

Perimeter=2(l+w)=2(12.00+10.40)=44.8cm

The number of significant digits in the result is 3.

The perimeter of red rectangle is calculated as shown below.

Perimeter=2(l+w)=2(20.20+2.42)=45.24cm

The number of significant digits in the result is 4.

The perimeter of green rectangle is calculated as shown below.

Perimeter=2(l+w)=2(3.18+2.55)=11.46cm

The number of significant digits in the result is 4.

The perimeter of orange rectangle is calculated as shown below.

Perimeter=2(l+w)=2(13.22+0.68)=27.8cm

The number of significant digits in the result is 3.

Conclusion

The areas of black, red, green and orange rectangles are 124.8cm2, 48.884cm2, 8.109cm2 and 8.9896cm2 respectively. The number of significant digits in the results is 4, 5, 4 and 5 respectively. The perimeters of black, red, green and orange rectangles are 44.8cm, 45.24cm, 11.46cm and 27.8cm respectively. The number of significant digits in the results is 3, 4, 4 and 3 respectively.

Interpretation Introduction

(b)

Interpretation:

The area and perimeter for each rectangle is to be calculated by changing all the measured values to meters and the results are to be expressed in square meters and meters respectively. The correct number of significant figures is to be stated.

Concept introduction:

In a number, the digits which express the accurate measurement of the number are known as significant figures. It is counted starting from the first non-zero digit in the given number. Zeroes that lie between two non-zero digits are considered significant. Zeroes at the end of a number are considered non significant in the absence of a decimal point, whereas they are considered significant if there is a decimal point after it. Zeroes after a decimal point are considered significant.

Expert Solution
Check Mark

Answer to Problem 1.76E

The areas of black, red, green and orange rectangles are 0.01248m2, 0.0048884m2, 0.0008109m2 and 0.00089896m2 respectively. The number of significant digits in the results is 4, 5, 4 and 5 respectively. The perimeters of black, red, green and orange rectangles are 0.448m, 0.4524m, 0.1146m and 0.278m respectively. The number of significant digits in the results is 3, 4, 4 and 3 respectively.

Explanation of Solution

It is known that 1cm=1100m.

The conversion of units of the dimensions of black rectangle is shown below.

l=12.00cm=12.00cm×1m100cm=0.12mw=10.40cm=10.40cm×1m100cm=0.1040m

The conversion of units of the dimensions of red rectangle is shown below.

l=20.20cm=20.20cm×1m100cm=0.2020mw=2.42cm=2.42cm×1m100cm=0.0242m

The conversion of units of the dimensions of green rectangle is shown below.

l=3.18cm=3.18cm×1m100cm=0.0318mw=2.55cm=2.55cm×1m100cm=0.0255m

The conversion of units of the dimensions of orange rectangle is shown below.

l=13.22cm=13.22cm×1m100cm=0.1322mw=0.68cm=0.68cm×1m100cm=0.0068m

The formula to calculate the area of a rectangle is given below.

Area=l×w …(1)

Where,

l is the length

w is the width

The area of black rectangle is calculated as shown below.

Area=l×w=0.12×0.1040=0.01248m2

The number of significant digits in the result is 4.

The area of red rectangle is calculated as shown below.

Area=l×w=0.2020×0.0242=0.0048884m2

The number of significant digits in the result is 5.

The area of green rectangle is calculated as shown below.

Area=l×w=0.0318×0.0255=0.0008109m2

The number of significant digits in the result is 4.

The area of orange rectangle is calculated as shown below.

Area=l×w=0.1322×0.0068=0.00089896m2

The number of significant digits in the result is 5.

The formula to calculate the perimeter of a rectangle is given below.

Perimeter=Sumofallfoursides=2(l+w) …(2)

Where,

l is the length

w is the width

The perimeter of black rectangle is calculated as shown below.

Perimeter=2(l+w)=2(0.1200+0.1040)=0.448m

The number of significant digits in the result is 3.

The perimeter of red rectangle is calculated as shown below.

Perimeter=2(l+w)=2(0.2020+0.0242)=0.4524m

The number of significant digits in the result is 4.

The perimeter of green rectangle is calculated as shown below.

Perimeter=2(l+w)=2(0.0318+0.0255)=0.1146m

The number of significant digits in the result is 4.

The perimeter of orange rectangle is calculated as shown below.

Perimeter=2(l+w)=2(0.1322+0.0068)=0.278m

The number of significant digits in the result is 3.

Conclusion

The areas of black, red, green and orange rectangles are 0.01248m2, 0.0048884m2, 0.0008109m2 and 0.00089896m2 respectively. The number of significant digits in the results is 4, 5, 4 and 5 respectively. The perimeters of black, red, green and orange rectangles are 0.448m, 0.4524m, 0.1146m and 0.278m respectively. The number of significant digits in the results is 3, 4, 4 and 3 respectively.

Interpretation Introduction

(c)

Interpretation:

Whether the number of significant figures gets changed on changing the units is to be stated.

Concept introduction:

In a number, the digits which express the accurate measurement of the number are known as significant figures. It is counted starting from the first non-zero digit in the given number. Zeroes that lie between two non-zero digits are considered significant. Zeroes at the end of a number are considered non significant in the absence of a decimal point, whereas they are considered significant if there is a decimal point after it. Zeroes after a decimal point are considered significant.

Expert Solution
Check Mark

Answer to Problem 1.76E

The number of significant figures does not change when the units of area and perimeter are changed.

Explanation of Solution

The number of significant figures does not change when the units of area and perimeter are changed from square centimeters and centimeters to square meters and meters respectively. Exact numbers possess infinite number of significant digits and these digits are not uncertain. Therefore, the number of significant digits in the final answer is not affected and they remain the same even after conversion of units.

Conclusion

The number of significant figures is not affected when the units of area and perimeter are changed from square centimeters and centimeters to square meters and meters respectively.

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